Abstract: The problem of adaptive generalized predictive control which consists of output prediction errors for a class of switched systems is studied. The switching law is determined by the output predictive errors of a finite number of subsystems. For the single subsystem and multiple subsystems cases, it is proved that the given direct algorithm of generalized predictive control guarantees the global convergence of the system. This algorithm overcomes the inherent drawbacks of the slow convergence and large transient errors for the conventional adaptive control.

Key words: global convergence, covering property, H-space, H-convex, H-convex hull, almost fixed point, lower semi-continuous, l.c.-space, simplex, uniform structure, topological vector space, locally convex space, contractible, generalized predictive control, switched system, adaptive control